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Arrive at the expression for kinetic ene...

Arrive at the expression for kinetic energy of particle executing SHM.

Text Solution

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`"K.E. of particle "=(1)/(2)m omega^(2)A^(2)-(1)/(2)m omega^(2)x^(2)`
`=(1)/(2)m omega^(2)(A^(2)-x^(2))`
`"where "x=Acos (omegat+phi)`
`"Also K.E."=(1)/(2)momega^(2)(A^(2))(1-cos^(2)(omegat+phi))`
`"i.e., K.E"=(1)/(2)m omega^(2)A^(2)sin^(2)(omegat+phi)`
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Knowledge Check

  • The total energy of a particle, executing S.H.M. is :

    A
    `prop X`
    B
    `prop X^(1//2)`
    C
    independent of X
    D
    `prop X^(2)` where X is the displacement from the mean position

  • Displacement between maximum potential energy position and maximum kinetic energy position for a particle executing S.H.M. is :

    A
    `+-(a)/(2)`
    B
    `+-a`
    C
    `+1`
    D
    `-1`

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